École Nationale Supérieure de
Techniques Avancées

Abstract

This report examines the efficiency of the finite element method in the context of data assimilation with a method based on a space-time variational formulation, the so-called 4d-var methods. Using a preliminary simulation based on the Laplacian equation, we evaluate the performance of this method on a simple mathematical problem. Next, we focus our analysis on the heat equation, aiming to determine how the finite element method performs in more complex scenarios compared to non-conforming methods. Through detailed experiments, we evaluate the performance of the finite element method in terms of accuracy and cost. This study offers an in-depth perspective on the advantages and limitations of the finite element method for solving data assimilation problems, and contributes to a better understanding of its potential in various scientific and engineering fields.